2021 Advanced topics in Algebra G1

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Academic unit or major
Graduate major in Mathematics
Instructor(s)
Suzuki Masatoshi 
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Mon5-6()  
Group
-
Course number
MTH.A507
Credits
1
Academic year
2021
Offered quarter
3Q
Syllabus updated
2021/3/19
Lecture notes updated
-
Language used
English
Access Index

Course description and aims

The theory of automorphic L-functions is a major research area of modern number theory and is nowadays becoming more and more important in several related areas of mathematics. This lecture aims to explain the basics of automorphic L-functions and to mention a recent breakthrough on the subconvexity problem. This course is followed by Advanced topics in Algebra H1.

Student learning outcomes

Students are expected to:
- obtain basic notions and methods related to automorphic L-functions,
- understand modern tools and concepts in the theory of automorphic L-functions,
- attain a deep understanding of the theory of automorphic L-functions.

Keywords

modular forms, automorphic representations, automorphic L-functions, subconvexity problem

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

This is a standard lecture course. There will be some homework assignments.

Course schedule/Required learning

  Course schedule Required learning
Class 1 The Riemann zeta function and Dirichlet L-functions Details will be provided during each class session
Class 2 The classical subconvexity problem Details will be provided during each class session
Class 3 Classical modular forms Details will be provided during each class session
Class 4 Adele rings and idele groups Details will be provided during each class session
Class 5 Dirichlet characters and representations of GL(1) Details will be provided during each class session
Class 6 Adelization of classical automorphic forms Details will be provided during each class session
Class 7 Automorphic forms and representations of GL(2) Details will be provided during each class session
Class 8 Whittaker model and Fourier expansion Details will be provided during each class session

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

None required.

Reference books, course materials, etc.

Details will be announced during the course.

Assessment criteria and methods

Course scores are evaluated by homework assignments (100%). Details will be announced during the course.

Related courses

  • MTH.A508 : Advanced topics in Algebra H1
  • MTH.A301 : Algebra I
  • MTH.A302 : Algebra II
  • MTH.C301 : Complex Analysis I
  • MTH.C302 : Complex Analysis II

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basic undergraduate algebra and complex analysis

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